1. **State the problem:** We are given the algebraic equation $$100 = 5x + 40$$ and need to identify which verbal situations correspond to this equation. 2. **Understand the equation:** The equation represents a total amount of 100, which is made up of a fixed amount 40 plus 5 times some variable $x$. 3. **Analyze each situation:** - Max has $5 in savings and adds $40 weekly: This would be $$\text{total} = 5 + 40x$$, not matching the equation. - Max has $40 in savings and adds $5 weekly: This matches $$100 = 5x + 40$$ where $x$ is weeks. - Sarah has 100 videos, 40 makeup, 5 other topics: Total videos = 40 + 5x, matches equation. - Sarah has 100 videos, 5 makeup, 40 other topics: Total = 5 + 40x, does not match. - Janice has $100 balance, pays $40 initially, then $5 weekly: Remaining balance after initial payment is $60, so total paid after $x$ weeks is $40 + 5x$, matching equation. - Janice has $40 balance, pays $100 initially: This is inconsistent with the equation. 4. **Conclusion:** The correct verbal situations are: - Max has $40 in savings and adds $5 weekly. - Sarah has 100 videos, 40 makeup, 5 other topics. - Janice has $100 balance, pays $40 initially, then $5 weekly. 5. **Final answer:** The equation $$100 = 5x + 40$$ models these three situations.